Hester makes one vague reference to Dimmesdale when Pearl asks her mother if she ever saw the black man of the forest. Hester is exasperated at Pearl's question so she says that she did meet "the black man" in the forest and the scarlet letter was his mark. This is an indirect, but misleading, way of telling Pearl that she met "the man in black", Dimmesdale, in the forest and that the scarlet letter, which Hester wore because she became pregnant with Pearl, was Dimmesdale's mark.
However, Hester never has to tell Pearl directly because Dimmesdale admits to it in front of her during the last scaffold scene. During that scene, he admits to being her father and asks her to kiss him now that he has made the admission. Although she had wiped off his kiss in the forest, she finally kisses him on the scaffold.
In the Chapter III, when Rev. Dimmesdale speaks to Hester, her baby that she clutches to her breast turns her "gaze towards Mr. Dimmesdale, and held up its little arms with a half-pleased, half-plaintive murmur." This reaction of baby Pearl indicates recognition of Dimmesdale as one who has held her before; she is acquainted with the minister.
In Chapter 15, Pearl notes a connection between her mother and the minister, asking what the scarlet letter on her mother's breast means and inquiring why the minister keeps his hand over his heart. She repeats these questions, an action which suggests that Pearl senses a connection of Rev. Dimmesdale to her mother. In Chapter 19 Pearl is called from across the brook to meet Hester and the Reverend: "Now she fixed her bright wild eyes on her mother, now on the minister, and now included them both in the same glance, as if to detect and explain to herself the relation which they bore to one another." When the minister involuntarily puts his hand over his heart, Pearl becomes agitated until Hester reclaims her discarded letter and restores it to her heart. It would seem, therefore, that Pearl intuitively understands the connection between her mother and Dimmesdale. On the holiday, Pearl asks why the minister does not acknowledge them in the daylight when he walked with them in the forest and even kissed her head. Pearl clearly senses her father as Dimmesdale; she kisses him in the end.